Updated On : August 7, 2023

The Indian Institute of Management (IIM) conducts the Integrated Program in Management Aptitude Test (IPMAT) annually for providing admission to the five-year integrated program in management.

Going through the previous year's paper analysis will let you understand better the essential topics to focus on more for better results.

Our experts at Supergards have curated the IPMAT Analysis and Solutions of the past five years in this post.

The takeaways from this post can immensely help you in streamlining your preparation to a result-oriented pathway and also get an idea about the number of questions asked from each subject, the difficulty level of the paper, type of questions, and more.

The following points explain the Past Five-year's** Exam Analysis of the IIM IPM Exam,** such as mode of exam, sections involved, nature of questions, and more.

**Type of questions:**Multiple Choice Questions MCQs and Short Answer (SA) questions.**Sections:**Generally, there are three sections in the exam. Two sections are of quantitative ability, and one is verbal ability.**Maximum Marks:**The is conducted for a total of 400 marks.**Marking scheme:**4 marks are awarded for every correct answer, one mark is deducted for every wrong answer in MCQs, and there is no negative marking in short answers.

**Sectional Cut-off:**It is applicable to all three sections.**Difficulty Level:**The overall difficulty level of IPMAT, considering previous years’ examination, is moderate to difficult.**Verbal Ability:**This is the most scoring section in the examination, with about 70-80% of questions from easy to moderate difficulty.**Quantitative Ability:**MCQ is generally the most challenging section, with about 40-50% moderate to complex questions.

As per the **Exam Pattern for IPMAT**, 50% of the question paper comprises the quantitative section (including MCQs and short answer-type questions).

- Generally, the SA section is of moderate difficulty having 20-30% tricky questions.
- Majorly, the questions are based on Logs, Arithmetic Progressions, Geometry, P&C, Probability.
- Statistically, 40% of questions are based on logarithms and Sequence & Series, and the same trend is followed from the past few years.
- A good attempt would be anything between 70-80% attempt with 80% accuracy.
- The pie chart plotted below represents an overall trend of the percentage of questions asked from different topics.

* Read more*:

- Generally, this section is the most difficult section having 40-50% tricky questions and 40 questions to be completed within 40 minutes.
- Majorly questions are based on Number Systems, Arithmetic, Algebra, Geometry and Menstruation, P & C, Sets, Data Interpretation, and Matrices.
- Statistically, 50-55% of questions are based on Algebra, Arithmetics, and Data Interpretation.
- A good attempt would be anything between 65-70% attempt with 85% accuracy, fetching you about 80-90 marks.
- The below pie chart represents an overall trend of the percentage of questions asked from different topics.

As per the previous year's trends, the IPMAT verbal ability section questions do not test your conventional English language or do not ask direct vocabulary questions like antonyms, synonyms, analogies, etc.

Instead, the verbal questions test your overall expertise in English with question types like usage of words & phrases, fill in the blanks, and your capability to use contextual vocabulary.

Check out the detailed IPMAT Question Paper analysis and solutions for the verbal ability section from the post below.

- Generally, this section is the easiest section having about 80% of questions of easy to moderate level difficulty.
- Majorly questions are based on Reading Comprehension, Fill in the blanks, Sentence Completion, Para Jumbles, and sentence completion-based questions.
- Statistically, 50-55% of questions are based on reading comprehension and fill-in blanks.
- A good attempt would be anything between 90% attempt with 85-90% accuracy, fetching you about 120-125 marks.
- The below pie chart represents an overall trend of the percentage of questions asked from different topics.

* Read more*:

To help you get an idea about the type of questions asked in the quantitative aptitude (short answer) section, we have provided a few sample questions that were curated from the **previous year's IPMAT question papers**.

Try to solve them for a better understanding of the difficulty level and the type of questions asked in the exam.

**Question 1: In a division problem, the product of quotients and the remainder is 24 while their sum is 10. If the divisor is 5 then the dividend is __________. (IPMAT 2020)**

**Solution 1 :**

In this problem, we have given that the product of quotient(q) and the remainder(r) is 24. i.e q x r = 24 -( i )

And it is also given that their sum is 10 i.e q + r = 10 -( ii )

Divisor(d) = 5.

( i ) and ( ii ) represent the sum and product of a quadratic equation, from ( ii ) putting r = q - 10, in ( i ), we will get q x (10 - q) = 24, i.e q^{2}-10q + 24 = 0, which will give

q = 6 or 4.

* Read more*:

Therefore one of them will be 6, and the other one will be 4. We do not know yet whether the quotient is 6 and the remainder is 4 or vice versa. We know that Dividend(n) = divisor(d) x quotient(q) + remainder(r) .

From the given data, n = 5 x q + r. - ( iii ),

As the divisor is 5, we infer that the remainder obviously will be smaller than 5. Therefore, the remainder will be 4, and the quotient will be 6. Putting the above-decided value in ( iii ). n = 5(6) + 4 , therefore n = 34.

**Question 2 : The shortest distance from the point (-4,3) to the circle x2 + y2 = 1 is __________. ( IPMAT 2020 )**

**Solution 2.**

In this question, we have been given the equation of a circle and the coordinates of a point.

From the standard equation of circle i.e x2 + y2 = a2, we have a = 1.

The shortest distance of the point P(-4, 3) will be the distance from point P to the point where a straight line drawn from P to the circle's origin intersects the circle. As shown in the figure below, the shortest distance is PM.

* Read more*:

**Question 3: The value of**

**Question 4: The minimum value of f(x)=|3-x|+|2+x|+|5-x| is equal to __________.**

**Solution. **

Form f(x)=|3-x|+|2+x|+|5-x| We know that critical points would be x = 3 , x = -2 , and x = 5.

The slope of the line changes at these critical points.

Example

Now we need to select the critical point which has the lowest value of y axis, from the figure above f(3) will have the lowest value.

f(3) = |3 - 3|+|2 + 3|+| 5 - 3|

f(3) = 0 + 5 + 2 .

f(3) = 7.

Hence the answer is **7.**

* Read more*:

**Question 5: Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio of 4: 1 and paid Rs. 112. The cost of a pen, as well as a pencil in rupees, is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________. (IPMAT 2020)**

**Solution.**

We have been given that when the person spends Rs. 86, the ratio of pen and pencil is 2:3.

And when he pays Rs. 112, the ratio of pen and pencil is 4:1. And in this visit, the total number of pens is 4.

Let x be the price per pen and y be the price per pencil.

Therefore we have

4x + y = 112

2x + 3y = 86 (From first visit)

It is in Ratios, so it can be 4x + 6y = 86 (or)

6x + 9y = 86 (or)

8x + 12y = 86 and so on.

As we know, 4x + y = 112, we can infer that 4x + 6y = 86 is not possible, and hence all the equations after this are not possible.

* Read more*:

So now we have 4x + y = 112

2x + 3y = 86

Solving the above equation we will get y = 12.

Therefore 4x + 12 = 112

=> 4x = cost of pens = 112 -12 = 100

Hence the answer is 100.

**Question 6: In a four-digit number, the product of thousands digit and units digit is zero while their difference is 7. The product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is __________.**

**Solution. **

Let the four-digit number be ABCD. D is the unit place number, C is the tens digit number, B is the hundreds digit number, and A is the thousand digit number.

Given data

- A x D = 0

This implies one of them will be zero; as A is the rightmost place, its value cannot be zero.

Therefore D = 0.

- A - D = 7

As D = 0, A will be 7.

- B x C = 18

B and C can hold values from 0-9 only; looking at the possible combinations, BC can be 92( or 29) or 63(or 36).

- Given that the AD difference is the same as the difference of BC, therefore, B is 9 and C is 2.

Hence the answer is 7920.

**Question 7: Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.**

**Solution. **

Let the speed of the fast one be 3x, and the speed of the slow one be 2x.

Time required for the fast one to cover one complete round = tf = 300/3x

Time required for the slow one to cover one complete round = ts = 300/2x

For finding out the time at which both meet for the first time, we need to find lcm of tf and ts

Tmeet = 300/x (lcm of tf and ts)

Distance traveled by the fast one when they meet = Tmeet * speed of fast one

= 300/x * 3x

= 900 m

Therefore they will first meet when the fast one has covered 900m; then they will meet at 1800, and then for the last at 2700 meters.

Therefore the winner will pass the slow one precisely 3 times.

In this section, the difficulty level of questions will be easy to moderate level of difficulty. Therefore, learning **Short tricks to Attempt Quantitative Aptitude Section** will help you fetch more marks than others.

Check out the questions that can be asked from the quantitative ability MCQ section from the post below.

**Question 1: The probability that a randomly chosen factor of 10****19**** is a multiple of 10****15**** is**

**1/25****1/12****1/20****1/16**

**Solution. **

Given number is 1019 , the factor of the given number are 219 x 519

Therefore the total factors of 1019 are (19 + 1)(19 + 1) = 400.

Multiples of 1015 are 215 x 515; This is of the form 2x × 5y

We need multiple numbers of 2x × 5y and a factor of 219 × 519. Therefore the possible values of x = 15 , 16 , 17 ,18 , 19

And possible values of y = 15 , 16 , 17 ,18 , 19

Therefore there are five possible values of x and five possible values of y.

Favourable outcome = 5 * 5 = 25

Total number of outcomes = 400

Probability = 25/400 = 1/16.

Hence the correct option is option D.

**Question 2: The number of acute-angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is**

**28****29****31****33**

**Solution.**

We have been given three conditions:-

- Triangle sides (a+b > c)
- Acute angle triangle (a2 + b2 > c2)
- Perimeter <= 100 (a + b + c <= 100)

Let's take random values for three consecutive integers: 1, 2, 3

This selection is impossible as it does not satisfy the first condition that the sum of two sides of a triangle should be greater than the third side. Therefore we rule this out. : 2, 3, 4

The first condition is satisfied, but the second condition, i.e., Acute angle property, is the sum of the square of any two sides has to be greater than the square of the third side 22 + 32 > 42

As 13 < 16. (So this condition is also not satisfied) : 3, 4, 5

The first condition is satisfied, but the second condition, i.e., Acute angle property, is the sum of the square of any two sides has to be greater than the square of the third side 32 + 42 > 52

As 25 = 25. (So this condition is also not satisfied) : 4, 5, 6

Since all the conditions mentioned above are satisfied, 4,5,6 will be our first consecutive integer set. Then (5,6,7) works and so on.

When the numbers become larger squares, they become increasingly larger

So after 4,5,6, all sets will satisfy condition 2.

Now we need to know the last possible consecutive number set based on the third condition.

Which gives 32,33,34 -Perimeter is at most 100

Therefore from the first 32 Combinations, the first 3 are ruled out. So in total, 29 combinations are possible.

Hence choice B is the correct answer.

* Read more*:

**Question3 : The value of cos****2** **/8****+ cos****2** **3****/8**** + cos****2** **5****/8**** + cos****2** **7****/8**** is.**

**1**

**3/2**

**2**

**9/4**

**Solution.**

We know that 58= 2 + 8

And 78= 2 + 38 =

=> cos2 /8+ cos2 3/8 + cos2 (/2 +/8 ) + cos2 (/2 +3/8)

=> cos2 /8+ cos2 3/8 + sin2 /8 + sin2 3/8

=> (cos2 /8+ sin2 /8 )+ (cos2 3/8 + sin2 3/8)

=> 1 + 1

=> 2

Hence the correct choice is option C.

**Q4. if ****1****1****2****+ ****1****2****2****+****1****3****2****+****1****4****2****+ ..... upto ****= ****2****6****, then the value of ****1****1****2****+****1****3****2****+****1****5****2****+ ..... upto ****, is.**

**2****/8**

**2****/16**

**2****/12**

**2****/36**

**Solution.**

Given 112+ 122+132+142+ ..... upto = 26 -(i)

Separation even and odd terms

(112+132+152+ ..... upto ) +(122+142+162+ ..... upto ) = 26

x + 1/4(112+ 122+132+142+ ..... upto ) = 26

x + 1/4(112+ 122+132+142+ ..... upto ) = 26

x + 1/4( 26) = 26 from (i)

x =26(1 - 14)

x =28

Hence the correct choice is option A.

**Question 5: A 2 × 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6}, Then the probability that the matrix generated in such a way is singular is**

**2/45**

**1/45**

**4/15**

**1/15**

**Solution.**

We know that the matrix will be singular only if its determinant is zero.

Therefore, the given matrix be

a |
c |

b |
c |

= |acdb| = ab - cd = 0, Or ab = cd

Using hit and trial from the given set {1,2,3,4,5,6}.

- Let one of a,b,c or d is 5, then ab ≠ cd, because in the given set {1,2,3,4,5,6} there is only one multiple of 5. So now we have to select 4 integers from {1,2,3,4,6}
- Let's take 3 or 6, since 6 is a multiple of 3 we will need to pick both of them. Therefore now the equation becomes 3b = 6d

* Read more*:

From the above equation we can infer that, b > d

{b, d} ⊂ {1, 2, 4}

If b = 4, d = 2

If b = 2, d = 1

Taking 3 and 6 we observed that only 2 choices were possible i.e {a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6}. Hence, we can select four numbers from the six in 6C4 = 15 ways

Therefore there will be 15 ways to select them and 4! ways to arrange them in the matrix.

So, the total number of matrices that can form is 15 x 4!.

Once we select {a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6}, for the matrix to be singular 2,3 or 4,3 should be on the same diagonal. Hence , only â…“ of the arrangements yield a singular matrix.

Only one-third of the arrangements yield a singular matrix, and the others don’t.

Probability of getting a singular matrix = 2( 4! â…“ )154! = 2/45.

Hence option A is the correct choice.

Here is a sample question from the verbal ability section of the IPMAT Exam. Try solving this question to know** how well you can attempt IPM Verbal Ability Questions**.

Along with this question, you are advised to practice more questions from previous year's papers to test your preparation levels.

**(Q.1 - 6)Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.**

Supposing half a dozen or a dozen men were cast ashore from a wreck on an uninhabited island and left to their own resources, one of course, according to his capacity, would be set to one business and one to another; the strongest to dig and to cut wood, and to build huts for the rest: the most dexterous to make shoes out of bark and coats out of skins; the best educated to look for iron or lead in the rocks, and to plan the channels for the irrigation of the fields. But though their labours were thus naturally severed, that small group of shipwrecked men would understand well enough that the speediest progress was to be made by helping each other-not by opposing each other. They would know that this help could only be properly given so long as they were frank and open in their relations, and the difficulties which each lay under properly explained to the rest. So that any appearance of secrecy or separateness in the actions of any of them would instantly, and justly, be looked upon with suspicion by the rest, as the sign of some selfish or foolish proceeding on the part of the individual. If, for instance, the scientific man were found to have gone out at night, unknown to the rest, to alter the sluices, the others would think, and in all probability rightly think, that he wanted to get the best supply of water to his own field; and if the shoemaker refused to show them where the bark grew which he made the sandals off, they would naturally think, and in all probability rightly think, that he didn't want them to see how much there was of it and that he meant to ask from them more corn and potatoes in exchange for his sandals than the trouble of making them deserved. And thus, although each man would have a portion of time to himself in which he was allowed to do what he chose without let or inquiry - so long as he was working in that particular business which he had undertaken for the common benefit, any secrecy on his part would be immediately supposed to mean mischief; and would require to be accounted for, or put an end to and this all the more because, whatever the work might be. Certainly there would be difficulties about it which, when once they were well explained, might be more or less done away with by the help of the rest; so that assuredly every one of them would advance with his labour not only more happily, but more profitably and quickly, by having no secrets, and by frankly bestowing, and frankly receiving, such help as lay in his way to get or to give.

**Q1. When a dozen men are cast away on an imaginary island, the best educated will look for metals in rocks because**

- Metals can be used to make weapons.
- Such an island probably has unexploited resources.
- He may find it beneath him to dig or cut or make shoes.
- He is suited for such work.

**Q2. The author states that any appearance of secrecy or separateness would instantly and justly be looked upon with suspicion. From this statement, we may infer that**

- what is secret is not what is separate
- secrecy is not the same as separateness
- it is natural to be suspicious of the secrecy
- it only takes an instant for a relationship to deteriorate

**Q3. The instance of the shoemaker who refuses to show his source and asks for more corn and potatoes is an example of**

- a strong bargain.
- Unfair practice.
- The system of barter.
- The intent to make trouble.

**Q4. According to the author, whatever one's work might be**

- Hardships are going to be part of it.
- One cannot keep complaining.
- One should expect others to assure of help and advance our labours.
- One must offer help to others in order to receive help.

* Read more*:

**Q5. The author's belief is that for progress to happen**

- A team should consist of people with multiple talents.
- Cooperation among team members is essential.
- One must deal with those who are secretive.
- Transparency among all concerned is mandatory.

**Q6. The writer makes a hypothesis, which can be related to**

- communities in general.
- An imaginary island, rich with resources.
- An ideal world of talented people.
- A primitive and unsophisticated world.

**Question: Rearrange the following sentences**

- A. Despite the strong performance of the economy in 2010-11, the outlook for 2011-12 is clouded by stubborn and persistently high inflation and rising external risks.
- B. The three key macroeconomic concerns before the Union Budget 2011-12 were high inflation, high current account deficit (CAD), and fiscal consolidation.
- C. Additionally, there was an expectation that the government would restart the reform process.
- D. While the Budget sets a lower nominal gross domestic product (GDP) growth target of 14%, we believe that the real GDP growth target of 9% factored in the Budget is optimistic.
- E. The Budget has attempted to address all these issues, albeit through small steps.

1. BCEAD

2. CBAED

3. DACEB

4. ADCEB

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August 7, 2023

The Indian Institute of Management (IIM) conducts the Integrated Program in Management Aptitude Test (IPMAT) annually for providing admission to the five-year integrated program in management.

Going through the previous year's paper analysis will let you understand better the essential topics to focus on more for better results.

Our experts at Supergards have curated the IPMAT Analysis and Solutions of the past five years in this post.

The takeaways from this post can immensely help you in streamlining your preparation to a result-oriented pathway and also get an idea about the number of questions asked from each subject, the difficulty level of the paper, type of questions, and more.

The following points explain the Past Five-year's** Exam Analysis of the IIM IPM Exam,** such as mode of exam, sections involved, nature of questions, and more.

**Type of questions:**Multiple Choice Questions MCQs and Short Answer (SA) questions.**Sections:**Generally, there are three sections in the exam. Two sections are of quantitative ability, and one is verbal ability.**Maximum Marks:**The is conducted for a total of 400 marks.**Marking scheme:**4 marks are awarded for every correct answer, one mark is deducted for every wrong answer in MCQs, and there is no negative marking in short answers.

**Sectional Cut-off:**It is applicable to all three sections.**Difficulty Level:**The overall difficulty level of IPMAT, considering previous years’ examination, is moderate to difficult.**Verbal Ability:**This is the most scoring section in the examination, with about 70-80% of questions from easy to moderate difficulty.**Quantitative Ability:**MCQ is generally the most challenging section, with about 40-50% moderate to complex questions.

As per the **Exam Pattern for IPMAT**, 50% of the question paper comprises the quantitative section (including MCQs and short answer-type questions).

- Generally, the SA section is of moderate difficulty having 20-30% tricky questions.
- Majorly, the questions are based on Logs, Arithmetic Progressions, Geometry, P&C, Probability.
- Statistically, 40% of questions are based on logarithms and Sequence & Series, and the same trend is followed from the past few years.
- A good attempt would be anything between 70-80% attempt with 80% accuracy.
- The pie chart plotted below represents an overall trend of the percentage of questions asked from different topics.

* Read more*:

- Generally, this section is the most difficult section having 40-50% tricky questions and 40 questions to be completed within 40 minutes.
- Majorly questions are based on Number Systems, Arithmetic, Algebra, Geometry and Menstruation, P & C, Sets, Data Interpretation, and Matrices.
- Statistically, 50-55% of questions are based on Algebra, Arithmetics, and Data Interpretation.
- A good attempt would be anything between 65-70% attempt with 85% accuracy, fetching you about 80-90 marks.
- The below pie chart represents an overall trend of the percentage of questions asked from different topics.

As per the previous year's trends, the IPMAT verbal ability section questions do not test your conventional English language or do not ask direct vocabulary questions like antonyms, synonyms, analogies, etc.

Instead, the verbal questions test your overall expertise in English with question types like usage of words & phrases, fill in the blanks, and your capability to use contextual vocabulary.

Check out the detailed IPMAT Question Paper analysis and solutions for the verbal ability section from the post below.

- Generally, this section is the easiest section having about 80% of questions of easy to moderate level difficulty.
- Majorly questions are based on Reading Comprehension, Fill in the blanks, Sentence Completion, Para Jumbles, and sentence completion-based questions.
- Statistically, 50-55% of questions are based on reading comprehension and fill-in blanks.
- A good attempt would be anything between 90% attempt with 85-90% accuracy, fetching you about 120-125 marks.

* Read more*:

To help you get an idea about the type of questions asked in the quantitative aptitude (short answer) section, we have provided a few sample questions that were curated from the **previous year's IPMAT question papers**.

Try to solve them for a better understanding of the difficulty level and the type of questions asked in the exam.

**Question 1: In a division problem, the product of quotients and the remainder is 24 while their sum is 10. If the divisor is 5 then the dividend is __________. (IPMAT 2020)**

**Solution 1 :**

In this problem, we have given that the product of quotient(q) and the remainder(r) is 24. i.e q x r = 24 -( i )

And it is also given that their sum is 10 i.e q + r = 10 -( ii )

Divisor(d) = 5.

( i ) and ( ii ) represent the sum and product of a quadratic equation, from ( ii ) putting r = q - 10, in ( i ), we will get q x (10 - q) = 24, i.e q^{2}-10q + 24 = 0, which will give

q = 6 or 4.

* Read more*:

Therefore one of them will be 6, and the other one will be 4. We do not know yet whether the quotient is 6 and the remainder is 4 or vice versa. We know that Dividend(n) = divisor(d) x quotient(q) + remainder(r) .

From the given data, n = 5 x q + r. - ( iii ),

As the divisor is 5, we infer that the remainder obviously will be smaller than 5. Therefore, the remainder will be 4, and the quotient will be 6. Putting the above-decided value in ( iii ). n = 5(6) + 4 , therefore n = 34.

**Question 2 : The shortest distance from the point (-4,3) to the circle x2 + y2 = 1 is __________. ( IPMAT 2020 )**

**Solution 2.**

In this question, we have been given the equation of a circle and the coordinates of a point.

From the standard equation of circle i.e x2 + y2 = a2, we have a = 1.

The shortest distance of the point P(-4, 3) will be the distance from point P to the point where a straight line drawn from P to the circle's origin intersects the circle. As shown in the figure below, the shortest distance is PM.

* Read more*:

**Question 3: The value of**

**Question 4: The minimum value of f(x)=|3-x|+|2+x|+|5-x| is equal to __________.**

**Solution. **

Form f(x)=|3-x|+|2+x|+|5-x| We know that critical points would be x = 3 , x = -2 , and x = 5.

The slope of the line changes at these critical points.

Example

Now we need to select the critical point which has the lowest value of y axis, from the figure above f(3) will have the lowest value.

f(3) = |3 - 3|+|2 + 3|+| 5 - 3|

f(3) = 0 + 5 + 2 .

f(3) = 7.

Hence the answer is **7.**

* Read more*:

**Question 5: Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio of 4: 1 and paid Rs. 112. The cost of a pen, as well as a pencil in rupees, is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________. (IPMAT 2020)**

**Solution.**

We have been given that when the person spends Rs. 86, the ratio of pen and pencil is 2:3.

And when he pays Rs. 112, the ratio of pen and pencil is 4:1. And in this visit, the total number of pens is 4.

Let x be the price per pen and y be the price per pencil.

Therefore we have

4x + y = 112

2x + 3y = 86 (From first visit)

It is in Ratios, so it can be 4x + 6y = 86 (or)

6x + 9y = 86 (or)

8x + 12y = 86 and so on.

As we know, 4x + y = 112, we can infer that 4x + 6y = 86 is not possible, and hence all the equations after this are not possible.

* Read more*:

So now we have 4x + y = 112

2x + 3y = 86

Solving the above equation we will get y = 12.

Therefore 4x + 12 = 112

=> 4x = cost of pens = 112 -12 = 100

Hence the answer is 100.

**Question 6: In a four-digit number, the product of thousands digit and units digit is zero while their difference is 7. The product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is __________.**

**Solution. **

Let the four-digit number be ABCD. D is the unit place number, C is the tens digit number, B is the hundreds digit number, and A is the thousand digit number.

Given data

- A x D = 0

This implies one of them will be zero; as A is the rightmost place, its value cannot be zero.

Therefore D = 0.

- A - D = 7

As D = 0, A will be 7.

- B x C = 18

B and C can hold values from 0-9 only; looking at the possible combinations, BC can be 92( or 29) or 63(or 36).

- Given that the AD difference is the same as the difference of BC, therefore, B is 9 and C is 2.

Hence the answer is 7920.

**Question 7: Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.**

**Solution. **

Let the speed of the fast one be 3x, and the speed of the slow one be 2x.

Time required for the fast one to cover one complete round = tf = 300/3x

Time required for the slow one to cover one complete round = ts = 300/2x

For finding out the time at which both meet for the first time, we need to find lcm of tf and ts

Tmeet = 300/x (lcm of tf and ts)

Distance traveled by the fast one when they meet = Tmeet * speed of fast one

= 300/x * 3x

= 900 m

Therefore they will first meet when the fast one has covered 900m; then they will meet at 1800, and then for the last at 2700 meters.

Therefore the winner will pass the slow one precisely 3 times.

In this section, the difficulty level of questions will be easy to moderate level of difficulty. Therefore, learning **Short tricks to Attempt Quantitative Aptitude Section** will help you fetch more marks than others.

Check out the questions that can be asked from the quantitative ability MCQ section from the post below.

**Question 1: The probability that a randomly chosen factor of 10****19**** is a multiple of 10****15**** is**

**1/25****1/12****1/20****1/16**

**Solution. **

Given number is 1019 , the factor of the given number are 219 x 519

Therefore the total factors of 1019 are (19 + 1)(19 + 1) = 400.

Multiples of 1015 are 215 x 515; This is of the form 2x × 5y

We need multiple numbers of 2x × 5y and a factor of 219 × 519. Therefore the possible values of x = 15 , 16 , 17 ,18 , 19

And possible values of y = 15 , 16 , 17 ,18 , 19

Therefore there are five possible values of x and five possible values of y.

Favourable outcome = 5 * 5 = 25

Total number of outcomes = 400

Probability = 25/400 = 1/16.

Hence the correct option is option D.

**Question 2: The number of acute-angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is**

**28****29****31****33**

**Solution.**

We have been given three conditions:-

- Triangle sides (a+b > c)
- Acute angle triangle (a2 + b2 > c2)
- Perimeter <= 100 (a + b + c <= 100)

Let's take random values for three consecutive integers: 1, 2, 3

This selection is impossible as it does not satisfy the first condition that the sum of two sides of a triangle should be greater than the third side. Therefore we rule this out. : 2, 3, 4

The first condition is satisfied, but the second condition, i.e., Acute angle property, is the sum of the square of any two sides has to be greater than the square of the third side 22 + 32 > 42

As 13 < 16. (So this condition is also not satisfied) : 3, 4, 5

The first condition is satisfied, but the second condition, i.e., Acute angle property, is the sum of the square of any two sides has to be greater than the square of the third side 32 + 42 > 52

As 25 = 25. (So this condition is also not satisfied) : 4, 5, 6

Since all the conditions mentioned above are satisfied, 4,5,6 will be our first consecutive integer set. Then (5,6,7) works and so on.

When the numbers become larger squares, they become increasingly larger

So after 4,5,6, all sets will satisfy condition 2.

Now we need to know the last possible consecutive number set based on the third condition.

Which gives 32,33,34 -Perimeter is at most 100

Therefore from the first 32 Combinations, the first 3 are ruled out. So in total, 29 combinations are possible.

Hence choice B is the correct answer.

* Read more*:

**Question3 : The value of cos****2** **/8****+ cos****2** **3****/8**** + cos****2** **5****/8**** + cos****2** **7****/8**** is.**

**1**

**3/2**

**2**

**9/4**

**Solution.**

We know that 58= 2 + 8

And 78= 2 + 38 =

=> cos2 /8+ cos2 3/8 + cos2 (/2 +/8 ) + cos2 (/2 +3/8)

=> cos2 /8+ cos2 3/8 + sin2 /8 + sin2 3/8

=> (cos2 /8+ sin2 /8 )+ (cos2 3/8 + sin2 3/8)

=> 1 + 1

=> 2

Hence the correct choice is option C.

**Q4. if ****1****1****2****+ ****1****2****2****+****1****3****2****+****1****4****2****+ ..... upto ****= ****2****6****, then the value of ****1****1****2****+****1****3****2****+****1****5****2****+ ..... upto ****, is.**

**2****/8**

**2****/16**

**2****/12**

**2****/36**

**Solution.**

Given 112+ 122+132+142+ ..... upto = 26 -(i)

Separation even and odd terms

(112+132+152+ ..... upto ) +(122+142+162+ ..... upto ) = 26

x + 1/4(112+ 122+132+142+ ..... upto ) = 26

x + 1/4(112+ 122+132+142+ ..... upto ) = 26

x + 1/4( 26) = 26 from (i)

x =26(1 - 14)

x =28

Hence the correct choice is option A.

**Question 5: A 2 × 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6}, Then the probability that the matrix generated in such a way is singular is**

**2/45**

**1/45**

**4/15**

**1/15**

**Solution.**

We know that the matrix will be singular only if its determinant is zero.

Therefore, the given matrix be

a |
c |

b |
c |

= |acdb| = ab - cd = 0, Or ab = cd

Using hit and trial from the given set {1,2,3,4,5,6}.

- Let one of a,b,c or d is 5, then ab ≠ cd, because in the given set {1,2,3,4,5,6} there is only one multiple of 5. So now we have to select 4 integers from {1,2,3,4,6}
- Let's take 3 or 6, since 6 is a multiple of 3 we will need to pick both of them. Therefore now the equation becomes 3b = 6d

* Read more*:

From the above equation we can infer that, b > d

{b, d} ⊂ {1, 2, 4}

If b = 4, d = 2

If b = 2, d = 1

Taking 3 and 6 we observed that only 2 choices were possible i.e {a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6}. Hence, we can select four numbers from the six in 6C4 = 15 ways

Therefore there will be 15 ways to select them and 4! ways to arrange them in the matrix.

So, the total number of matrices that can form is 15 x 4!.

Once we select {a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6}, for the matrix to be singular 2,3 or 4,3 should be on the same diagonal. Hence , only â…“ of the arrangements yield a singular matrix.

Only one-third of the arrangements yield a singular matrix, and the others don’t.

Probability of getting a singular matrix = 2( 4! â…“ )154! = 2/45.

Hence option A is the correct choice.

Here is a sample question from the verbal ability section of the IPMAT Exam. Try solving this question to know** how well you can attempt IPM Verbal Ability Questions**.

Along with this question, you are advised to practice more questions from previous year's papers to test your preparation levels.

**(Q.1 - 6)Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.**

Supposing half a dozen or a dozen men were cast ashore from a wreck on an uninhabited island and left to their own resources, one of course, according to his capacity, would be set to one business and one to another; the strongest to dig and to cut wood, and to build huts for the rest: the most dexterous to make shoes out of bark and coats out of skins; the best educated to look for iron or lead in the rocks, and to plan the channels for the irrigation of the fields. But though their labours were thus naturally severed, that small group of shipwrecked men would understand well enough that the speediest progress was to be made by helping each other-not by opposing each other. They would know that this help could only be properly given so long as they were frank and open in their relations, and the difficulties which each lay under properly explained to the rest. So that any appearance of secrecy or separateness in the actions of any of them would instantly, and justly, be looked upon with suspicion by the rest, as the sign of some selfish or foolish proceeding on the part of the individual. If, for instance, the scientific man were found to have gone out at night, unknown to the rest, to alter the sluices, the others would think, and in all probability rightly think, that he wanted to get the best supply of water to his own field; and if the shoemaker refused to show them where the bark grew which he made the sandals off, they would naturally think, and in all probability rightly think, that he didn't want them to see how much there was of it and that he meant to ask from them more corn and potatoes in exchange for his sandals than the trouble of making them deserved. And thus, although each man would have a portion of time to himself in which he was allowed to do what he chose without let or inquiry - so long as he was working in that particular business which he had undertaken for the common benefit, any secrecy on his part would be immediately supposed to mean mischief; and would require to be accounted for, or put an end to and this all the more because, whatever the work might be. Certainly there would be difficulties about it which, when once they were well explained, might be more or less done away with by the help of the rest; so that assuredly every one of them would advance with his labour not only more happily, but more profitably and quickly, by having no secrets, and by frankly bestowing, and frankly receiving, such help as lay in his way to get or to give.

**Q1. When a dozen men are cast away on an imaginary island, the best educated will look for metals in rocks because**

- Metals can be used to make weapons.
- Such an island probably has unexploited resources.
- He may find it beneath him to dig or cut or make shoes.
- He is suited for such work.

**Q2. The author states that any appearance of secrecy or separateness would instantly and justly be looked upon with suspicion. From this statement, we may infer that**

- what is secret is not what is separate
- secrecy is not the same as separateness
- it is natural to be suspicious of the secrecy
- it only takes an instant for a relationship to deteriorate

**Q3. The instance of the shoemaker who refuses to show his source and asks for more corn and potatoes is an example of**

- a strong bargain.
- Unfair practice.
- The system of barter.
- The intent to make trouble.

**Q4. According to the author, whatever one's work might be**

- Hardships are going to be part of it.
- One cannot keep complaining.
- One should expect others to assure of help and advance our labours.
- One must offer help to others in order to receive help.

* Read more*:

**Q5. The author's belief is that for progress to happen**

- A team should consist of people with multiple talents.
- Cooperation among team members is essential.
- One must deal with those who are secretive.
- Transparency among all concerned is mandatory.

**Q6. The writer makes a hypothesis, which can be related to**

- communities in general.
- An imaginary island, rich with resources.
- An ideal world of talented people.
- A primitive and unsophisticated world.

**Question: Rearrange the following sentences**

- A. Despite the strong performance of the economy in 2010-11, the outlook for 2011-12 is clouded by stubborn and persistently high inflation and rising external risks.
- B. The three key macroeconomic concerns before the Union Budget 2011-12 were high inflation, high current account deficit (CAD), and fiscal consolidation.
- C. Additionally, there was an expectation that the government would restart the reform process.
- D. While the Budget sets a lower nominal gross domestic product (GDP) growth target of 14%, we believe that the real GDP growth target of 9% factored in the Budget is optimistic.
- E. The Budget has attempted to address all these issues, albeit through small steps.

1. BCEAD

2. CBAED

3. DACEB

4. ADCEB

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